/// <summary>
/// Create a finite field GF(2^m)
/// </summary>
///
/// <param name="Degree">The degree of the field</param>
public GF2mField(int Degree)
{
if (Degree >= 32)
{
throw new ArgumentException("Error: the degree of field is too large!");
}
if (Degree < 1)
{
throw new ArgumentException("Error: the degree of field is non-positive!");
}
this._degree = Degree;
_polynomial = PolynomialRingGF2.GetIrreduciblePolynomial(Degree);
}
/// <summary>
/// Create a finite field GF(2^m) with the fixed field polynomial
/// </summary>
///
/// <param name="Degree">The degree of the field</param>
/// <param name="Polynomial">The field polynomial</param>
public GF2mField(int Degree, int Polynomial)
{
if (Degree != PolynomialRingGF2.Degree(Polynomial))
{
throw new ArgumentException(" Error: the degree is not correct!");
}
if (!PolynomialRingGF2.IsIrreducible(Polynomial))
{
throw new ArgumentException(" Error: given polynomial is reducible!");
}
_degree = Degree;
_polynomial = Polynomial;
}
/// <summary>
/// Create a finite field GF(2^m) using an encoded array
/// </summary>
///
/// <param name="Encoded">The polynomial and degree encoded as a byte array</param>
public GF2mField(byte[] Encoded)
{
if (Encoded.Length != 4)
{
throw new ArgumentException("byte array is not an encoded finite field");
}
_polynomial = LittleEndian.OctetsToInt(Encoded);
if (!PolynomialRingGF2.IsIrreducible(_polynomial))
{
throw new ArgumentException("byte array is not an encoded finite field");
}
_degree = PolynomialRingGF2.Degree(_polynomial);
}
/// <summary>
/// Return the product of two elements
/// </summary>
///
/// <param name="A">Integer value A</param>
/// <param name="B">Integer value b</param>
///
/// <returns>The sum: <c>a*b</c></returns>
public int Multiply(int A, int B)
{
return(PolynomialRingGF2.ModMultiply(A, B, _polynomial));
}
